Practice Higher-order Non-homogeneous Equations (6.5) - Non-Homogeneous Equations

Practice: Higher-Order Non-Homogeneous Equations

Lesson 6.5Non-Homogeneous Equations

Practise this section

8 questions

Flashcard drill
3 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
2 questions · about 1 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
What does the term non-homogeneous imply in differential equations?
Show hintHide hint
Think about forces acting on a physical system.
Question 2.
What is the first step in solving a higher-order non-homogeneous equation?
Show hintHide hint
What do we look at when external forces are removed?
3Question 3.
What is the general form of a higher-order linear non-homogeneous equation?
- $\\frac{d^2y}{dx^2} + ay = f(x)$
- $\\frac{d^n y}{dx^n} + a_{n-1} \\frac{d^{n-1}y}{dx^{n-1}} + ... + a_0y = f(x)$
- $y'' + by' + cy = 0
Show hintHide hint
Look for derivatives of order $n$ and the non-homogeneous term.
4Question 4.
True or False: The Complementary Function is the solution of the non-homogeneous part.
- True
- False
Show hintHide hint
Remember the difference between homogenous and non-homogeneous.
Question 5.
Given the fourth-order equation $\frac{d^4y}{dx^4} + 6\frac{d^2y}{dx^2} + 9y = x^2 - 3$ , determine the general solution.
Show hintHide hint
Remember your roots and how they impact the CF's form!
Question 6.
How does the system's behavior change if we alter $f(x)$ from $cos(ωx)$ to a more complex function? Explain its impact on resonance and equations.
Show hintHide hint
Focus on how frequency aligns with the system's response!

4 more questions in this section. Enroll free to practise them all.